A test for a local formation of finite groups to be a formation of soluble groups with the Shemetkov property

2024/05/30 by Murashka, V. I.
#20D10 #20F19 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2405.20257

Abstract

L.A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local formations \mathfrakF of finite groups such that every finite minimal non-\mathfrakF-group is either a Schmidt group or a group of prime order. All known solutions to this problem are obtained under the assumption that every minimal non-\mathfrakF-group is soluble. Using the above mentioned solutions we present a polynomial in n time check for a local formation \mathfrakF with bounded π(\mathfrakF) to be a formation of soluble groups with the Shemtkov property where n=max π(\mathfrakF).

Related

• Constructing regular saturated formations of finite soluble groups
• Formations of Finite Groups in Polynomial Time: the \mathfrakF-Hypercenter
• Localizations of finitely generated soluble groups
• Local definitions of formations of finite groups
• Formations of Finite Groups in Polynomial Time: \mathfrakF-residuals and \mathfrakF-subnormality